Etch profiles in silicon in SF ₆ and O ₂ plasma based on etch-depth-dependent O/F transport gradient model

Abstract This study quantitatively investigates the “bowing” mechanism in high-aspect-ratio (HAR) silicon etching using SF 6 /O 2 inductively coupled plasmas through a multi-scale simulation. By integrating reactor-scale and feature-scale modeling, we analyzed the dynamic radical balance at the etch front. Results provide numerical proof for the “transport gradient model,” demonstrating that the localized O/F flux ratio [%]—accounting for Knudsen transport and sticking probabilities—is the decisive factor for sidewall protection, advancing the qualitative O/F intensity ratio from our previous work. We identified a critical threshold for this flux ratio between 3.5% and 3.6%. Below this threshold, the surface coverage transitions from oxygen-dominant to fluorine-dominant, triggering a nonlinear surge in the chemical etching rate. This explains why the 30% O 2 condition maintains verticality at shallow depths, while the 20% O 2 condition causes immediate bowing. These findings provide a theoretical foundation for optimizing radical fluxes in high-fidelity HAR etching.